Non-commutative Hermite--Pad\'{e} approximation and integrability

Autor:	Doliwa, Adam
Rok vydání:	2022
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics Mathematics - Numerical Analysis
Zdroj:	Lett. Math. Phys. 112 (2022) 68
Druh dokumentu:	Working Paper
DOI:	10.1007/s11005-022-01560-z
Popis:	We introduce and solve the non-commutative version of the Hermite-Pad\'{e} type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to a subclass of solutions of the non-commutative Hirota (discrete Kadomtsev--Petviashvili) system and of its linear problem. We also prove integrability of the constrained system, which in the simplest case is the non-commutative discrete-time Toda lattice equation known from the theory of non-commutative Pad\'{e} approximants and matrix orthogonal polynomials. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.00782 Zobrazit plný text záznamu View this record from Arxiv